First and second order velocity shifts and reflection coefficients for periodic interdigital transducers by boundary condition matching

Abstract

The method of boundary condition matching is utilized to determine reflection coefficients and velocity shifts for surface acoustic wave devices mechanically and electrically loaded by a periodic grating. The method has previously been limited to grooved gratings in isotropic substrates, but is here extended to allow for anisotropic and piezoelectric substrates as well as arbitrary overlay materials which allows for the modeling of metallic electrode interdigital transducers. Upper and lower stop band frequencies are determined by imposing the proper grating boundary conditions. From these frequencies is calculated both first and second order contributions in h/λ (where h is the grating finger height and λ the wavelength) to the reflection coefficient and velocity shift due to the loading of the substrate. The presence of the grating also couples the incident surface acoustic waves to evanescent and bulk modes. The attenuation of the incident Rayleigh waves due to bulk mode conversion is discussed as well. Numerical results for some common substrate and overlay materials are given and a comparison of the relative strengths of the first and second order contributions for specific values of h/λ is made. Some comparisons with experimental data are also given with good results for sufficiently small h/λ.